By Saturday morning, every major league team will have played its first game of the 2012 season. That includes opening day in Japan (March 28), opening night in North America (April 4), opening day in North America (April 5) and opening day for everyone else in North America (April 6).

But although every team is gearing up for action, not every player is so fortunate. Whether by choice or by circumstances beyond their control, 10 veteran players who have become household names during their careers remain unsigned.

Those 10, listed in order by the likelihood of them landing a deal:

SP Roy Oswalt. After not landing the deal he was seeking (with the St. Louis Cardinals or Texas Rangers), he announced earlier this spring that he planned to sit out the first part of the season. He should be on a major league mound by June, if not sooner.

DH/OF Johnny Damon. Agent Scott Boras told ESPN.com on Monday that Damon will sign with a team by May 1. However, Boras isn’t sure which team it will be, creating plenty of doubt about whether he and Damon have any serious leads at this point.

DH/OF Vladimir Guerrero. He recently worked out for the Cleveland Indians, who need more offense but apparently don’t need another one-dimensional DH. Unless a situation presents itself soon in the majors, Vlad could shop himself to teams in Japan.

C Ivan Rodriguez. There appeared to be some interest from the Kansas City Royals when starting catcher Salvador Perez was lost to knee surgery, but the team then traded for backup Humberto Quintero.

3B Miguel Tejada. He was unceremoniously booted from the San Francisco Giants early last September and has drawn very little interest since then. In February, he expressed a desire to return to the Oakland A’s, with whom he started his career. That feeling wasn’t mutual, even though the team lost starting third baseman Scott Sizemore to a season-ending knee injury.

DH Hideki Matsui. Like Guerrero, he is limited by his inability to play outfield and could consider ending his career where he began it: Japan. The Yankees and A’s both had some level of interest in bringing him back but ultimately went in different directions.

SS/2B Edgar Renteria. He reportedly turned down a pair of minor league contracts, one of which was from the Milwaukee Brewers. He appears headed toward retirement, by his own choice.

1B Derrek Lee. Like Renteria, he appears content with hanging up his cleats. There has been very little chatter about Lee this spring despite the fact that he was targeted by several teams at the trading deadline last July.

OF/DH Magglio Ordonez. He attempted a comeback but recently tweeted that he is close to announcing his retirement. Teams apparently aren’t willing to gamble on his troublesome ankles.

SP Javier Vazquez. Even before the 2011 season ended, Vazquez admitted he was leaning heavily toward retirement. On Monday, he told MLB.com that nothing has changed, though he has yet to officially call it quits.